numbers unit test
8. evaluate.
a) $\frac{1}{3} + \frac{1}{4}$ b) $\frac{7}{8} - \frac{2}{4}$
c) $5 \times \frac{5}{7} =$
9. create a factor tree for the numbers below.
81 120
10. a hen named betty lays 6 eggs in 8 days. another hen named doris lays 12 eggs in 15 days. which hen lays eggs at a faster rate? show your thinking.
good work!

Question

numbers unit test
8. evaluate.
 a) $\frac{1}{3} + \frac{1}{4}$  b) $\frac{7}{8} - \frac{2}{4}$
 c) $5 \times \frac{5}{7} =$
9. create a factor tree for the numbers below.
 81  120
10. a hen named betty lays 6 eggs in 8 days. another hen named doris lays 12 eggs in 15 days. which hen lays eggs at a faster rate? show your thinking.
good work!

Accepted Answer

### 8a)
# Explanation:
## Step1: Find a common denominator.
The common denominator of 3 and 4 is 12. So we rewrite the fractions: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$.
## Step2: Add the fractions.
$\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}$.
# Answer:
$\frac{7}{12}$

### 8b)
# Explanation:
## Step1: Find a common denominator.
The common denominator of 8 and 4 is 8. Rewrite $\frac{2}{4}$ as $\frac{4}{8}$.
## Step2: Subtract the fractions.
$\frac{7}{8} - \frac{4}{8} = \frac{7 - 4}{8} = \frac{3}{8}$.
# Answer:
$\frac{3}{8}$

### 8c)
# Explanation:
## Step1: Multiply the integer by the numerator.
$5 	imes \frac{5}{7} = \frac{5 	imes 5}{7}$.
## Step2: Calculate the numerator.
$5 	imes 5 = 25$, so the result is $\frac{25}{7}$.
# Answer:
$\frac{25}{7}$ (or $3\frac{4}{7}$)

### 9. Factor Trees
#### For 81:
# Explanation:
## Step1: Start with 81.
81 can be factored into $9 	imes 9$.
## Step2: Factor 9.
Each 9 can be factored into $3 	imes 3$. So the factor tree for 81 is:
$81$
$\swarrow$  $\searrow$
$9$    $9$
$\swarrow$ $\searrow$  $\swarrow$ $\searrow$
$3$  $3$  $3$  $3$
So the prime factorization of 81 is $3^4$.

#### For 120:
# Explanation:
## Step1: Start with 120.
120 can be factored into $12 	imes 10$.
## Step2: Factor 12 and 10.
12 factors into $4 	imes 3$, and 10 factors into $2 	imes 5$. Then 4 factors into $2 	imes 2$. So the factor tree for 120 is:
$120$
$\swarrow$  $\searrow$
$12$    $10$
$\swarrow$ $\searrow$  $\swarrow$ $\searrow$
$4$  $3$  $2$  $5$
$\swarrow$ $\searrow$
$2$  $2$
So the prime factorization of 120 is $2^3 	imes 3 	imes 5$.

### 10. Egg - Laying Rate
# Explanation:
## Step1: Calculate Betty's rate.
Betty lays 6 eggs in 8 days. Her rate is $\frac{6}{8} = \frac{3}{4}$ eggs per day (simplify by dividing numerator and denominator by 2).
## Step2: Calculate Doris's rate.
Doris lays 12 eggs in 15 days. Her rate is $\frac{12}{15} = \frac{4}{5}$ eggs per day (simplify by dividing numerator and denominator by 3).
## Step3: Compare the rates.
We need to compare $\frac{3}{4}$ and $\frac{4}{5}$. Find a common denominator, which is 20. $\frac{3}{4} = \frac{15}{20}$ and $\frac{4}{5} = \frac{16}{20}$. Since $\frac{16}{20} > \frac{15}{20}$, $\frac{4}{5} > \frac{3}{4}$.
# Answer:
Doris lays eggs at a faster rate because her rate of $\frac{4}{5}$ (or 0.8) eggs per day is greater than Betty's rate of $\frac{3}{4}$ (or 0.75) eggs per day.

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QUESTION IMAGE

Question

Explanation:

8a)

Step1: Find a common denominator.

Step2: Add the fractions.

Step1: Find a common denominator.

Step2: Subtract the fractions.

Step1: Multiply the integer by the numerator.

Step2: Calculate the numerator.

Answer:

8b)